FISHER in Google Sheets: Transform Correlations Safely
Apply the Fisher transformation in Google Sheets, check it with logarithms, transform a paired-data correlation and avoid endpoint and interpretation mistakes.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =FISHER(0.6) has expected result 0.6931471806. FISHER transforms a value on the correlation scale to Fisher’s z scale. It does not calculate a correlation from raw data and does not return a p-value.
Syntax and mathematical meaning
=FISHER(value)
The single required argument is the value to transform. Google’s FISHER reference documents this one-argument function and points to PEARSON, CORREL and FISHERINV as related functions. There are no optional arguments or documented defaults.
The real-valued Fisher transformation, also defined in the NIST Dataplot reference, is:
z = 0.5 × ln((1 + r) / (1 - r))
For a finite real answer, use −1 < r < 1. The argument is a correlation-like numeric value, not a percentage entered on a 0–100 scale. A correlation of 0.6 may be displayed as 60%, but the number 60 is outside this transform’s real domain.
The formula is nonlinear and unbounded near the endpoints. Positive inputs give positive outputs, negative inputs give negative outputs, and zero maps to zero. These mathematical properties are useful diagnostic checks.
Worked example: direct transformations
Enter the following values in A1:A5. Put the heading Fisher z in B1.
| Cell | Value |
|---|---|
| A1 | Correlation |
| A2 | 0.6 |
| A3 | 0 |
| A4 | −0.6 |
| A5 | 0.8 |
In B2 enter and fill down through B5:
=FISHER(A2)
Expected results:
| Cell | Expected result, rounded |
|---|---|
| B2 | 0.6931471806 |
| B3 | 0 |
| B4 | −0.6931471806 |
| B5 | 1.0986122887 |
The first result is half the natural logarithm of 4. The last is half the natural logarithm of 9. The transform preserves ordering but does not preserve distances: the difference between transformed values is not a difference measured in correlation points.
Independent formula and inverse checks
With the original A2 = 0.6, enter in C2:
=0.5*LN((1+A2)/(1-A2))
Expected result: 0.6931471805599453 to typical floating-point display precision. This exposes the mathematical calculation used to derive the expected answer.
To return to the original scale, use Google’s separately documented FISHERINV function:
=FISHERINV(B2)
Expected result: approximately 0.6. A tiny difference in the final displayed digits can arise in floating-point calculations. Compare a suitable tolerance rather than requiring the text representation of every digit to be identical.
The inverse check must use the transformed value B2. Applying FISHERINV directly to A2 = 0.6 answers a different calculation; it does not leave 0.6 unchanged.
Advanced application: transform a correlation from paired observations
On a clear area or a fresh sheet, enter this complete table in A1:B6:
| Row | A: Predictor | B: Response |
|---|---|---|
| 1 | Predictor | Response |
| 2 | 1 | 2 |
| 3 | 2 | 4 |
| 4 | 3 | 5 |
| 5 | 4 | 4 |
| 6 | 5 | 5 |
In D2 calculate the correlation, then transform it in D3:
=PEARSON(A2:A6,B2:B6)
=FISHER(D2)
Expected D2: 0.7745966692. Expected D3: 1.0317185344. The corresponding single formula is:
=FISHER(PEARSON(A2:A6,B2:B6))
The independent correlation check uses centered cross-product sum 6, predictor squared-deviation sum 10, and response squared-deviation sum 6. Thus r = 6/√60, and applying the log transformation gives the stated z.
Keep observations aligned by row. Reordering one column separately changes the pairs and therefore changes the correlation. Missing values also require a deliberate paired-data policy. The tiny example demonstrates formula composition, not reliable evidence of a population relationship or causation.
Endpoints, rounding and interpretation
For r = 0.99, the expected transform is about 2.6466524124. For r = 0.9999, it is about 4.9517187756. Rounding either stored input to 1 before transformation destroys its finite value: the denominator in the log ratio becomes zero.
A cell displaying 1.00 might still store 0.9999. Inspect additional decimals or the formula bar before deciding that the underlying correlation is exactly 1. Do not clamp or alter a valid coefficient merely to make a formula run without documenting that change.
Fisher’s z here is a transformed correlation. It is not automatically a standard-normal test statistic. Statistical inference additionally needs a suitable sampling model, sample size and other assumptions. Averaging transformed correlations also does not, by itself, reproduce the correlation of pooled raw observations.
Troubleshooting
- If the calculation fails, confirm the input is numeric and strictly within the real domain.
- If the sign looks wrong, check whether the source correlation is negative and whether columns were paired correctly.
- If values look unexpectedly large, inspect closeness to −1 or 1 before treating that as an error.
- If raw data were passed directly, calculate the intended correlation first; FISHER accepts one value, not two data ranges.
- If the result appears as a percentage, change the display to a number. Fisher z is not a percentage probability.
The reviewed Google function page does not enumerate native error tokens, string coercions or handling of empty references. Those outcomes have not been inferred from another application. This guide’s domain guidance follows the real mathematical transformation; invalid-input behavior remains a separate native test question.
Availability and verification
FISHER is documented in Google’s rolling Sheets service. The checked references do not establish an original introduction date or a last functioning numbered release. Exporting to another spreadsheet requires checking that product’s function support and imported input precision.
NOT_TESTED_IN_GOOGLE_SHEETS. The individual Google documentation was inspected on October 17, 2026. All numeric results above are independent calculations, including the paired-data correlation; there was no Google Sheets execution or screenshot.